Linearization of Virasoro symmetries associated with semisimple Frobenius manifolds

2021/09/04 by Siqi Liu, Si-Qi Liu, Zhe Wang +4 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.2109.01846

openalex publication_date 2021/09/04 · arxiv created 2021/09/07 · arxiv updated 2021/09/08 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28

Abstract

For any semisimple Frobenius manifold, we prove that a tau-symmetric bihamiltonian deformation of its Principal Hierarchy admits an infinite family of linearizable Virasoro symmetries if and only if all the central invariants of the corresponding deformation of the bihamiltonian structure are equal to (1)/(24). As an important application of this result, we prove that the Dubrovin-Zhang hierarchy associated with the semisimple Frobenius manifold possesses a bihamiltonian structure which can be represented in terms of differential polynomials.

Citations

• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one

Cited by

• Open Hurwitz numbers and the mKP hierarchy

Related

• Generalized Frobenius Manifolds with Non-flat Unity and Integrable Hierarchies
• Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures
• The Virasoro-like Algebra of a Frobenius Manifold
• Tau function of the CKP hierarchy and non-linearizable Virasoro symmetries
• Frobenius Manifolds And Virasoro Constraints